Phenomenological perspective on mathematics education

This is a philosophical essay on a phenomenological way to understand and to work out Mathematics Education. Its philosophical grounding is the Husserlian work, focusing on its key word "going to the things themselves" in order to keep us away from the theoretical educational truth, took as the unique one. We assume the attitude of being on the life-world with the students and Mathematics as a field of research and practice that show and express themselves through lived experiences and through language. We assume to be in search of understanding of education, learning and Mathematics, as we take care, consciously, of what we are doing and saying in the same movement of saying and doing it.

On the injectivity of C1 maps of the real plane

Let X : ℝ2 → ℝ2 be a C1 map. Denote by Spec(X) the set of (complex) eigenvalues of DXp when p varies in ℝ2. If there exists ε > 0 such that Spec(X) ∩ (-ε, ε) = ∅, then X is injective. Some applications of this result to the real Keller Jacobian conjecture are discussed.

Connection space approach to ambiguities of gauge theories

Two distinct gauge potentials can have the same field strength, in which case they are said to be copies of each other. The consequences of this ambiguity for the general affine space A of gauge potentials are examined. Any two potentials are connected by a straight line in A, but a straight line going through two copies either contains no other copy or is entirely formed by copies. Copyright © 2005 Hindawi Publishing Corporation.

How to drag with a worn-out mouse? Searching for social justice through collaboration

We consider what a concern for social justice in terms of social inclusion might mean for teacher education, both practising and prospective, with particular reference to the use of information and communication technology (ICT) in mathematics education taking place at a borderland school. Our discussion proceeds through the following steps: (1) We explore what a borderland position might denote to address what social inclusion might mean. (2) We consider the significance of mathematics education and the use of ICT for processes of social inclusion. (3) We briefly refer to the Interlink Network, as many of our observations emerge as reflections on this project. (4) We present different issues that will be of particular importance with respect to teacher education if we want to establish a mathematics education for social inclusion. These issues concern moving away from the comfort zone, establishing networks, identifying new approaches, moving beyond prototypical research, and getting in contact. This brings us to (5) final considerations, where we return to the notion of social justice. © Springer Science+Business Media B.V. 2009.

Potential scenarios for Internet use in the mathematics classroom

Research on the influence of multiple representations in mathematics education gained new momentum when personal computers and software started to become available in the mid-1980s. It became much easier for students who were not fond of algebraic representations to work with concepts such as function using graphs or tables. Research on how students use such software showed that they shaped the tools to their own needs, resulting in an intershaping relationship in which tools shape the way students know at the same time the students shape the tools and influence the design of the next generation of tools. This kind of research led to the theoretical perspective presented in this paper: knowledge is constructed by collectives of humans-with-media. In this paper, I will discuss how media have shaped the notions of problem and knowledge, and a parallel will be developed between the way that software has brought new possibilities to mathematics education and the changes that the Internet may bring to mathematics education. This paper is, therefore, a discussion about the future of mathematics education. Potential scenarios for the future of mathematics education, if the Internet becomes accepted in the classroom, will be discussed. © FIZ Karlsruhe 2009.

Morphological routine proposal to extraction of highways in digital images of high resolution

This research proposes to apply techniques of Mathematics Morphology to extract highways in digital images of high resolution, targeting the upgrade of cartographic products. Remote Sensing data and Mathematical Morphological techniques were integrated in the process of extraction. Mathematical Morphology's objective is to improve and extract the relevant information of the visual image. In order to test the proposed approach some morphological operators related to preprocess, were applied to the original images. Routines were implemented in the MATLAB environment. Results indicated good performances by the implemented operators. The integration of the technologies aimed to implement the semiautomatic extraction of highways with the purpose to use them in processes of cartographic updating.

Uma caracterização do Centro de Educação Matemática - CEM (1984-1997) como uma Comunidade de prática de formação continuada de professores de matemática

This paper presents some results of a study on the Centre for Mathematics Education (Centro de Educação Matemática, CEM), a group of mathematics educators from the city of São Paulo-SP (Brazil), active mainly during the years 1984 to 1997. To establish a position on the process of identity constitution of CEM, we bring forth the method of Oral History and theories of identity. In this essay, an exercise in constituting the identity of CEM from the characterisation of this community's publications within its practice, we assume that the processes of identity constitution do not refer to what CEM is or was, but rather to a set of possibilities for apprehending it on the basis of strategies and initiatives set in given historical conditions and times. We make explicit three aspects that are present as their practice is converted into a source of coherence (mutual commitment, joint enterprise and shared repertoire), which allow one to reveal actions and production in the history of mathematics teacher education in the metropolitan region of São Paulo.

Boundary of the rauzy fractal sets in ℝ×ℂgenerated by p(x) = x 4- x 3 - x 2 -x- 1

We study the boundary of the 3-dimensional Rauzy fractal ε ⊂ ℝ×ℂ generated by the polynomial P(x) Dx 4-x 3-x 2-x-1. The finite automaton characterizing the boundary of ε is given explicitly. As a consequence we prove that the set ε has 18 neighboors where 6 of them intersect the central tile ε in a point. Our construction shows that the boundary is generated by an iterated function system starting with 2 compact sets.

Wavelets in a problem of signal processing

In this work a new method is proposed for noise reduction in speech signals in the wavelet domain. The method for signal processing makes use of a transfer function, obtained as a polynomial combination of three processings, denominated operators. The proposed method has the objective of overcoming the deficiencies of the thresholding methods and the effective processing of speech corrupted by real noises. Using the method, two speech signals are processed, contaminated by white noise and colored noises. To verify the quality of the processed signals, two evaluation measures are used: signal to noise ratio (SNR) and perceptual evaluation of speech quality (PESQ).

História da Matemática em contextos da Educação Matemática: contribuições do GPHM

In this article we tried to show the paths outlined during the past years by the Research Group on History of Mathematics and/or its relations with Mathematics Education (GPHM) at UNESP in Rio Claro - Brazil, as well as the contributions we believe we have made to Mathematics Education. The group's production has focused on issues that address the history of institutions and characters, linked to the history of disciplines, concepts and learning materials. Also, in broader terms of mathematics education, this article presents results from research that supports the understanding of teachers' conceptions about the use of History of Mathematics in the classroom; material on the history of mathematics accessible to the teacher; the presence of the history of mathematics in textbooks; proposed introductions of real numbers; and the subject of Analysis in teacher education and training.

A Prática do Professor que Ensina Matemática e a Colaboração: uma reflexão a partir de processos formativos virtuais

This text presents some reflections about the educational and virtual processes of mathematics teachers drawing on research on the theme. Thus, in this text, considering our experiences with the development of online courses, we discuss issues such as collaboration in virtual environments, which contributes to more effective results in collaborative learning and reduces the potential of isolation of student/teacher that can occur in virtual environments. Through collaborative learning in a virtual community, students/teachers have the opportunity to practice and think in-depth about their learning experiences by sharing new ideas with the group and receiving critical and constructive feedback. Moreover, the virtuality formed by the environment of online courses supports educational spaces for teachers who teach mathematics. Thus, collaboration emerges as an essential element for construction of meanings and for sharing experiences on the practice of teaching.

O jogo e a educação matemática: um estudo sobre as crenças e concepções dos professores de matemática quanto ao espaço do jogo no fazer pedagógico

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A metodologia de resolução de problemas: concepções e práticas pedagógicas de professores de matemática do ensino fundamental

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Alguns reflexos da didática construtivista no ensino de matemática nas quatro séries iniciais do Ensino Fundamental

Pós-graduação em Educação para a Ciência - FC